[Paper Review] Will Kinematic Sunyaev-Zel'dovich Measurements Enhance the Science Return from Galaxy Redshift Surveys?

Naonori S. Sugiyama, Teppei Okumura+1 more|arXiv (Cornell University)|Jun 20, 2016

Astronomy and Astrophysical Research4 citations

TL;DR

This paper demonstrates that combining kinematic Sunyaev-Zel'dovich (kSZ) measurements with galaxy redshift surveys significantly enhances cosmological constraints on the growth rate $f$ and Hubble parameter $H$. By modeling the anisotropic pairwise kSZ power spectrum up to the octopole and marginalizing over uncertain optical depth $\tau_{\rm T}$, the authors show that joint analysis reduces 1-$\sigma$ errors on $H$ and $f$ by 50–70% compared to galaxy surveys alone.

ABSTRACT

Yes. Future CMB experiments such as Advanced ACTPol and CMB-S4 should achieve measurements with S/N of $> 0.1$ for the typical galaxies in redshift surveys. These measurements will provide complementary measurements of the growth rate of large scale structure $f$ and the expansion rate of the Universe $H$ to galaxy clustering measurements. This paper emphasizes that there is significant information in the anisotropy of the relative pairwise kSZ measurements. We expand the relative pairwise kSZ power spectrum in Legendre polynomials and consider up to its octopole. Assuming that the noise in the filtered maps is uncorrelated between the positions of galaxies in the survey, we derive a simple analytic form for the power spectrum covariance of the relative pairwise kSZ temperature in redshift space. While many previous studies have assumed optimistically that the optical depth of the galaxies $\ au_{\ m T}$ in the survey is known, we marginalize over $\ au_{\ m T}$, to compute constraints on the growth rate $f$ and the expansion rate $H$. For realistic sure parameters, we find that combining kSZ and galaxy redshift survey data reduces the marginalized $1$-$\\sigma$ errors on $H$ and $f$ by $\\sim50$-$70\\%$ compared to the galaxy-only analysis.

Motivation & Objective

• To assess whether kSZ measurements from future CMB experiments can improve cosmological constraints from galaxy redshift surveys.
• To model the anisotropic relative pairwise kSZ power spectrum in redshift space, including up to the octopole moment.
• To derive an analytic covariance matrix for the kSZ power spectrum under realistic noise assumptions.
• To marginalize over uncertain optical depth $\tau_{\rm T}$ to obtain robust constraints on $f$ and $H$.
• To quantify the improvement in error constraints when combining kSZ and galaxy clustering data.

Proposed method

• Expand the relative pairwise kSZ temperature in Legendre polynomials up to $\ell=3$ to capture anisotropic clustering effects.
• Derive an analytic expression for the power spectrum covariance under the assumption of uncorrelated noise between galaxy positions.
• Use Fisher matrix analysis to compute parameter constraints, with partial derivatives of power spectra w.r.t. $D_{\rm A}$, $H$, $f$, $b$, and $\tau_{\rm T}$.
• Model the linear Kaiser bias and velocity bias in redshift space using $K_\ell^{(n)}$ factors to relate halo and matter power spectra.
• Assume $\vec{v} \propto f$ for peculiar velocities, consistent with General Relativity, and derive $\partial P / \partial \ln f$ from simulated power spectra.
• Compute marginalized errors on $H$ and $f$ by integrating over $\tau_{\rm T}$, avoiding the optimistic assumption that $\tau_{\rm T}$ is known.

Experimental results

Research questions

• RQ1 Can kSZ measurements from future CMB experiments like Advanced ACTPol and CMB-S4 provide meaningful cosmological constraints?
• RQ2 How does the anisotropy of the relative pairwise kSZ signal—up to the octopole—enhance constraints on $f$ and $H$?
• RQ3 What is the impact of marginalizing over uncertain optical depth $\tau_{\rm T}$ on the final error budget for $H$ and $f$?
• RQ4 To what extent does combining kSZ and galaxy redshift survey data reduce uncertainties compared to galaxy clustering alone?
• RQ5 How do redshift-space distortions affect the interpretation of kSZ-based velocity measurements?

Key findings

• Future CMB experiments such as Advanced ACTPol and CMB-S4 are expected to achieve signal-to-noise ratios >0.1 for typical host halos in redshift surveys.
• The anisotropic kSZ signal, particularly up to the octopole, contains significant cosmological information beyond the monopole.
• By marginalizing over $\tau_{\rm T}$, the joint analysis reduces 1-$\sigma$ errors on $H$ and $f$ to 50–70% of the errors from galaxy-only analysis.
• The derived analytic covariance matrix enables robust Fisher matrix forecasts for kSZ power spectra in redshift space.
• The method accounts for redshift-space distortions and velocity bias, improving the accuracy of $f$ and $H$ constraints.
• The results show that kSZ measurements provide complementary and powerful constraints on the growth rate and expansion rate, enhancing the science return from galaxy redshift surveys.